New Sochi - Novorossiysk sea route has been recently lunched for summer season. It will operate daily, except Mondays, between June 15th and August 31st. The hydrofoil (called Kometa, or Comet, in Russian ) trip lasts approximately 3 hours, and the ticket prices are: adult ticket is around $60 (1365 rubbles); kids older than 5yrs old – around $45 (1023 rubles), and kids under five with parents ride for free.

Here’s scheduler for Sochi/Novorossiysk route:

From Novorossiysk to Sochi, daily except Mondays:
Leaving: 9:00 (9:00am)
Arriving: 12:15 (12:15pm)

From Sochi to Novorossiysk, daily except Mondays:
Leaving: 18:00 (6:00pm)
Arriving: 21:15 (9:15pm)

Phone numbers in Novorossiysk port (probably only in Russian):

Ticketing in Novorossiysk Sea Port: (8617)-60-22-84
General Information: (8617)-60-23-24
Information in Novorossiysk Sea Port: (8617)-60-23-47

Btw, there are also daily buses going from Novorossiysk to Sochi, two leaving in the morning (7:50 & 10:50), and one at night (21:50). Information phone number: (8617)-64-42-79.

By far the most common way (the only way?) to enter Abkhazia from Russia is through Sochi. For a while foreigners (except Russian citizens and members of UN) were not able to enter Abkhazia. I don’t know when it has changed, but it is not a problem now — just make sure you have multiple entry Russian visa. The only way out of Abkhazia is back to Russia, as transit to Georgia is not permitted by Abkhazian government. Actually, I’ve heard of charter boats between Abkhazia and Turkey, but I don’t know what’s the deal there.

This good information shared Sergei Bagapsh, the President of Abkhazia during an interview to the Russia’s biggest online news source Lenta.ru

Sergei Bagapsh: Citizens of third countries can enter Abkhazia with out any problems. If a tourist has multiple entry Russian visa, he can come to Abkhazia with it as well. Many foreigners visit Abkhazia these days.

Link on topic: Official website of the President of Abkhazia.